Does the human lifespan have an impenetrable biological upper limit which ultimately will stop further increase in life lengths? This question is important for understanding aging, and for society, and has led to intense controversies. Demographic data for humans has been interpreted as showing existence of a limit, or even as an indication of a decreasing limit, but also as evidence that a limit does not exist. This paper studies what can be inferred from data about human mortality at extreme age. We find that in western countries and Japan and after age 110 the risk of dying is constant and is about 47% per year. Hence data does not support that there is a finite upper limit to the human lifespan. Still, given the present stage of biotechnology, it is unlikely that during the next 25 years anyone will live longer than 128 years in these countries. Data, remarkably, shows no difference in mortality after age 110 between sexes, between ages, or between different lifestyles or genetic backgrounds. These results, and the analysis methods developed in this paper, can help testing biological theories of aging and aid confirmation of success of efforts to find a cure for aging.A discussion of this paper will follow in a later issue of Extremes Electronic supplementary material The online version of this article (https://doi